The sensory receptor (hair) cells of auditory, vesibular and lateral-line organs are stimulated by displacements of bundles of sensory hairs that protrude from the cells' surfaces. Experiments show that the mechanics of hair bundle motion plays a key role in sensory reception in these systems, and hence, in the processes of hearing and equilibrium. Our goal is to understand the motions of hair bundles in terms of underlying physical mechanisms. In this application, we propose theoretical studies to assess how the motion of hair bundles is affected by: (1) cochlear fluids; (2) hydrodynamic coupling to nearby structures (such as the tectorial membrane and the surface of sensory epithelium); (3) hydrodynamic interactions with neighboring hair bundles; (4) the shape of the hair bundle; (5) mechanical properties of hair bundles, the tectorial membrane, and the sensory epithelium. The proposed theoretical studies will involve both mathematical analysis and numerical studies using a variety of digital computers (including personal computers, minicomputers, as well as supercomputers). Our approach is to examine solutions of the equations of fluid motion for a succession of geometries each designed to reveal the role of a key structural feature of hair cell organs.